A methodology for reliability assessment of structural systems subjected to seismic risk is developed. Based on modern concepts of structural reliability theory, structural safety against earthquakes is described through a performance function of ground motion variables. A multivariate risk analysis is then performed to compute the failure probability. The method can be applied to any type of structural system for which a performance function can be formulated. A specific application to linear structures using the response spectrum of ground motion is developed where the performance function is shown to be of quadratic form in terms of spectral ordinates. This application is illustrated through a numerical example for a two-degree-of-freedom structure with multiple failure modes. The example is also used to examine the accuracy of a conventional method that uses marginal probabilities to approximate a joint distribution.